The Curvature Fitting Game

The amount of curvature that appears in a photograph of a sphere depends on 1. The radius of the sphere, 2. Camera distance from the sphere, 3. Field of view of the camera, and 4. The distortion characteristic of the camera being used.

The ‘curvature fitting game’ has been flat-Earthers’ favorite pastime. They would try to fit a photograph of Earth’s curvature with another. If they find the result is not proportionally correct, they will make fun of it. They are wrong. Two different photos of a sphere can be taken differently and would show a different curve, even if the object being photographed is the same object.

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Magnetic Dip

Magnetic dip is the angle between the horizontal and Earth’s magnetic field. A compass needle, for example, will not point north and south, but will also have a dip. It tends to dip at an angle toward the Earth (and to the sky). The dip is generally greater toward the pole.  At various locations close to the equator (but not exactly at the equator), the dip is zero.

Magnetic dip as observed on various locations on Earth can only happen if the Earth is spherical.

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Airborne Early Warning & Control (AEW&C): Mitigating Limited Radar Range Due to Earth’s Curvature

An AEW&C (airborne early warning and control) system is a radar system attached to an aircraft. It can detect objects at a very long range compared to any surface mounted radar system.

The reason is that Earth’s curvature limits the range of a surface-based radar. An airborne radar system mitigates this problem.

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The Dip of the Horizon

There are two kinds of the horizon:

  • Astronomical horizon: the horizon at the eye level.
  • True horizon: the line that visually divides the Earth and the sky.

Because the Earth is a sphere, the true horizon always lies below the astronomical horizon, or the eye-level. The angle between them is the dip of the horizon. The higher the observer, the larger the dip of the horizon.

Flat-Earthers claim there’s no dip of the horizon. They are wrong. It is not hard to observe the drop of the horizon and prove the curvature of the Earth.

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Crow’s Nest on Ships

A crow’s nest is a structure in the upper part of the ship, especially old-fashioned ones. It is used as a lookout point and positioned high above to increase visibility over the curvature of the Earth.

On the deck of a ship 4 m (13 ft) above the surface of the ocean, an observer can spot a 20 m (66 ft) high ship from at most ±25 km (16 mi). On the other hand, from a 35 m (115 ft) high crow’s nest, an observer will be able to spot the same ship from ±40 km (25 mi) away.

On modern ships, the role of a lookout is replaced by radars. And for the same reason, a radar is positioned in the upper part of a ship.

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Shadow on Clouds

Before sunrise or after sunset, the Sun is below the horizon and not directly visible. But the sky and clouds above are illuminated because they are high above, and sunlight can reach them.

If there’s a mountain between the Sun and the clouds, it can cast a shadow on the clouds. The flat-Earth model assumes the Sun is always high above, and thus, this phenomenon cannot possibly occur in a flat-Earth.

The fact that a mountain can cast its shadow on clouds far above it is evidence that the Earth is spherical.

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A Glass of Water

The surface of the water in a glass of water is practically flat. Some flat-Earthers claim this is ‘evidence’ that the surface of the water is flat, and it will always be flat no matter how wide the container. They are wrong.

If the Earth is a sphere with the radius of 6371 km (3960 miles), then the surface of the water in a 10 cm (4 in) wide glass will have a bulge of 0.00000002 cm as the result of gravity, excluding other effects like the surface tension.

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Evidence of Curvature: Turning Torso Building, Malmö, Sweden

Turning Torso is a 190 m (623 ft) high building in Malmö, Sweden. It is situated near the strait of Øresund. At the other side of the channel lies the city of Copenhagen, Denmark, only 15 km (9 miles) away from Malmö. Turning Torso has a distinctive segmented shape that is easy to recognize from far. And more importantly for our purposes, the segmented form is making it easy to judge its height from far.

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The Reason We Cannot See Earth’s Curvature When Standing on a Beach

We can’t directly observe and subjectively perceive the curvature of the Earth from a position close to the surface. And this matches the expectations in the spherical Earth model.

Flat-Earthers often take the fact we can see the curvature by standing on a beach as ‘evidence’ the curve doesn’t exist. They are, once again, wrong.

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Curvature Calculators and Atmospheric Refraction

Atmospheric refraction causes a distant object to appear higher than its actual position. As a result, the object can be physically behind Earth’s curvature but is still visible because the light coming from it is refracted by the atmosphere.

There are many curvature calculators and simulation tools that don’t account for refraction. They would give us the correct results indicating the object’s physical positions but fail to show us the correct apparent position of the object when visually observed.

Flat-Earthers are often too happy with the calculator showing them the results they want to see and fail to see the reason for the discrepancy.

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Water Level Demonstrates The Dip of the Horizon and Proves Earth’s Curvature

As the Earth is spherical, the horizon is below the eye-level (or the astronomical horizon). The angle between the eye-level and the horizon is the dip of the horizon. The angle becomes larger as we go higher.

Flat-Earthers often claim that “the horizon always rises to eye-level”, and thus ‘proving’ the flat Earth claim. Despite their insistence to use a water level to ‘prove’ water is flat, the same device can be used to demonstrate the dip of the horizon, proving the water surface has curvature, and consistent with the spherical Earth model.

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Perspective Compression: Determining If a Curvature Exists

Soundly’s pictures and videos of Lake Pontchartrain power lines and causeway stirred up the flat-Earthers’ nests. They clearly show the curvature of the Earth, where it is usually hard to discern. For the rest of us, those pictures are just the consequence of the fact that the Earth is a globe.

Flat-Earthers can’t take this, and they invented various excuses to attack the credibility of these pictures and videos. Some of them look for specific vantage point where it is impossible or very hard to discern the curvature.  They would conclude if the curve is not seen from these vantage points, then it should not be visible from Soundly’s viewpoints.

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Curvature of the Horizon in High-Altitude Balloon Footage

High-altitude balloon footage is often abused by flat-Earthers to show us that the Earth is flat when seen from a high altitude.

We analyzed more than two dozens of footage taken from high-altitude balloons on YouTube, and we can easily conclude the curvature is there and usually easy to spot, including in the cases where flat-Earthers use the video as ‘proof’ of a flat Earth.

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The Eratosthenes Experiment: Proving the Earth is Spherical

In 205 BC, Eratosthenes successfully determined the circumference of the Earth by measuring the length of the shadow cast by a rod. He did the measurement in Alexandria and timed it to coincidence when the Sun is directly overhead Syene.

2222 years after that, some flat-Earthers tried to refute the Eratosthenes experiment. They say the experiment can be applied to the flat-Earth model.

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The Curvature of the Water Surface

Flat-Earthers mention the curvature of water a lot. According to them, the curve of the water can never be observed, and thus, the Earth is flat.

The problem with such an argument is that they usually conclude that from a very small amount of water. Water in a glass or a bucket will practically look flat. Not because there is no curvature due to Earth’s gravity, but because the water is in such small amount so that the curvature is minuscule and impossible to observe, let alone with the naked eye.

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